We model inter- and intra-layer interactions using a non-orthogonal tight-binding (TB) model with one orbital per carbon site, based on Reich et al. [1]}, Laissardiere et al. [2]}, and Bonnet et al. [3]}.
We extend the model to include curvature effects, using pp\(\sigma \)  interactions in addition to the pp\(\pi \)  interactions, and interlayer hopping to third nearest neighbors. The interlayer interaction ranges up to a cut-off distance of 5 and is described by exponential decays:
\(H_{pp\sigma /\pi }(d) &= H^{inter}_{pp\sigma /\pi } e^{\frac{(d-a_0)}{g_{pp\sigma /\pi }}} \\S_{pp\sigma /\pi }(d) &= S^{inter}_{pp\sigma /\pi } e^{\frac{(d-a_0)}{h_{pp\sigma /\pi }}} ,\) 
